Command examples by model¶

Supported models and scope · Shared syntax and precision · Plotted tutorials

These are entry commands, not a complete option or state-family catalogue. Use each model guide and the executable's --help for supported regimes and valid table names. Commands assume installed executables on PATH.

Model-specific entry points¶

These notes highlight differences from the XXX example, not every available program. See the supported-model index and overview for additional models and thermodynamic tools.

Spin-1/2 chains¶

bethe-xxx-pbc is the periodic XXX front end. For free-end OBC, use the separate bethe-xxx-obc program described in the open-chain guide.

For anisotropy, use bethe-xxz-pbc or the free-end bethe-xxz-obc; both require --delta. Both support ground states and sector minima for finite \(\Delta \ge 0\); their excitation and specified-real-root modes still require \(0\le \Delta \le 1\). Massive free-end ground states report an explicit boundary-root coordinate where needed; see the boundary-root guide.

Hubbard electrons¶

For electrons, bethe-hubbard-pbc requires --u and supports either sign of the interaction on even rings. Select --particles N and --sz VALUE; the defaults remain N=L and Sz=0. See the supported sector families before choosing a doped sector.

For free ends, bethe-hubbard-obc supports every physical N and Sz, odd or even L, and either sign of U. It defaults to N=L and the smallest nonnegative Sz compatible with N (0 or 1/2).

Continuum gases¶

For continuum bosons, bethe-lieb-liniger-pbc takes the particle count as its positional argument and requires --length ELL --c C. Its excitation scans also require a finite --padding P window; continuum momentum is not reduced to a Brillouin zone.

For spin-1/2 continuum fermions, bethe-gaudin-yang-pbc takes N and requires --length ELL --c C. Select the populations with --sz; interacting mixed-spin sectors require odd populations of both spins. The free and fully polarized limits also support other populations.

For more than two continuum fermion components, bethe-sun-fermions-pbc takes --populations N1,N2,... --length ELL --c C. Every occupied interacting population must be odd; free and single-component limits allow any counts. --roots displays all nested seas, with the physical-to-nesting component mapping retained in the report.

Supersymmetric t–J chain¶

For projected lattice electrons, bethe-tj-pbc fixes t=1, J=2 and takes L with optional --particles N --sz VALUE. It supports doped sectors with odd populations of both spins, plus every no-hole or fully polarized sector. Defaults are N=L and the smallest nonnegative Sz compatible with N. Explicit --precision bits-N or digits-N is supported with Uni20 MPFR scalars, including all three existing branches and root exports.

SU(3)/ULS and spin-1 TB chains¶

For three-state sites, bethe-su3-pbc takes L divisible by three and selects the balanced SU(3) singlet ground state of H=sum P. It reports two nested rapidity families; arbitrary sectors and finite-ring excitations are not yet available in that frontend. bethe-su3-dispersion provides thermodynamic elementary lines and two-/four-soliton continuum bounds, with optional three-site-cell folding.

For the spin-1 bilinear–biquadratic TB point, bethe-tb-pbc takes even L>=4 and selects the zero-field singlet ground state of H=sum[S.S-(S.S)^2]. Its --roots report retains finite deviations and the real and imaginary parts of each rapidity. bethe-tb-dispersion instead supplies infinite-chain spinon lines and two-/four-spinon bounds, with explicit spin labels and optional two-site momentum folding.

Biquadratic chains and TL modules¶

For the pure spin-1 biquadratic chain, bethe-biquadratic-obc takes even N>=2 and selects the free-end singlet ground state of H=-sum(S.S)^2 by default. --through-lines selects a TL module, --sectors lists module minima, and --excitations COUNT|all scans the restricted real-root family (default through-lines=2). The output includes physical multiplicities, not a decomposition into SU(2) multiplets.

Its --roots output belongs to the auxiliary XXZ model with opposite end fields, not the physical spin-1 chain. The Q-system and two-string singlet modes include selected complex roots.

With --ferromagnetic, the excitation tools also offer an analytic one-defect band and targeted bound pairs/triples. Ferro real-root scans accept odd/even N; --real-window WIDTH restricts --excitations to a high-label scattering window.

For mixed bound-pair-plus-defect states, use --pair-defect I1,...,Ir,J or --pair-defects COUNT|all --real-defects R (default R=1). The latter can restrict all label ranges with --mixed-window WIDTH. Both fix ell=N-2(R+2); these are not full module spectra, and partial scans return exit 2. Explicit --quantum-numbers also accepts odd N; AF ground/sector and Q-system modes retain their even-N restriction.

Pairing and central spin¶

For reduced BCS pairing, bethe-richardson requires --levels E0,E1,... --pairs M --g G, with optional zero-based --blocked indices. Levels are single-particle energies; g>=0 is attractive. This is not a chain, so no boundary suffix or lattice momentum applies. Use --variables for regularized eigenvalue variables, not pair rapidities.

For the rational central-spin model, bethe-central-spin requires --couplings A1,A2,... --field B --sz SZ. All spins are 1/2 and Sz includes the central spin. Distinct nonzero couplings and the field can have either sign; exactly zero field is supported. This nonspatial model also has no boundary suffix; --variables prints regularized variables.

Integrable ladder¶

For Wang's integrable ladder, bethe-ladder-pbc takes the number of rungs L>=2 and requires --rung JR. The leg coefficient is 1 and the four-spin coefficient is fixed at 4; this is not an ordinary Heisenberg ladder. Use --singlets NS for one singlet-count sector or --sectors for all sector minima; triplet populations are minimized too. --roots prints the selected state's highest-weight representative and retains the distinction between it and a physical SU(4) descendant. The frontend supports explicit bits-N/digits-N precision with Uni20 MPFR scalars, including fixed singlet and magnetization sectors and partial scans.

Sine-Gordon field theory¶

For sine-Gordon excitations, bethe-sine-gordon-dispersion --p P supplies particle lines and pair thresholds; bethe-sine-gordon-bethe-yang --p P --length L supplies asymptotic same-charge pair levels for P>=1. The latter omits wrapping corrections and is distinct from the finite-volume vacuum calculation.

bethe-sine-gordon-excited --p P --length L --number 0.5 instead solves the exact two-hole NLIE for P>=1, I=0.5 or 1.5. Its gap table subtracts a separately converged vacuum; use --csv-table gap=gap.csv to export that table directly.

bethe-kondo-response also accepts bits-N and digits-N with Uni20 MPFR scalars enabled. Its series and quadrature budgets remain separate from the arithmetic precision; see Kondo controls.

Hubbard thermodynamic MPFR uses explicit precision for quadrature and extrema. All paths need MPFR scalars; doped dispersion backgrounds use normal Uni20 CPU/provider LU dispatch. See Hubbard dispersions.

bethe-tasep-pbc accepts bits-N and digits-N with Uni20 MPFR/MPC scalars, using normal CPU/provider LU dispatch. Seed and Newton work budgets remain independent of arithmetic precision; see TASEP.

bethe-asep-pbc also accepts explicit MPFR precision for its TASEP seed and continuation; see ASEP controls and shared seeds.